Zeszyty Naukowe Politechniki Częstochowskiej nr 26 (2020), 60-65 DOI: 10.17512/znb.2020.1.09
A calculation of the load bearing capacity of glulam beams
with BFRP reinforcement
Damian Jończyk
1ABSTRACT:
Strengthening timber elements using fiber composites increasingly being used in construction. Despite the increasing popularity of this solution, there are still no normative provisions. The article discusses the effectiveness of the most common method used to determine the load capacity of glued laminated tim-ber beams reinforced with BFRP materials. Load capacity values, calculated analytically, were compared with the values determined in experimental tests. The method presented in the article may be helpful from an engineering perspective.
KEYWORDS:
timber; fiber composites; BFRP; analytical calculations
1. Introduction
The calculation of timber elements reinforced with FRP materials is not regulated in Poland. An important issue in the design of elements, for which there are no normative provisions, is the possibility of using existing calculation algorithms to assess the load capacity. It is impor-tant that in the case of this type of calculation method, the complexity of both assumptions and mathematical calculation procedures should be small. Jasieńko [1] presented analytical meth-ods for estimating the load-bearing capacity of timber elements reinforced with steel and attached wooden elements, while Nowak [2] reinforced with composites. Nowak also proposed a proprietary method for estimating the load capacity of timber beams reinforced with CFRP tapes. Currently, the literature usually presents methods using surrogate geometric and material characteristics [3] and the method based on the balance of forces in the cross section, such as presented in [4, 5].
The aim of the article is to assess the usefulness of the analytical method in estimating the load capacity of glued laminated timber, reinforced with BFRP bars.
2. Methodology 2.1. Experiment
For the analysis of analytically calculated values, the data presented in article [6] was used. The cited publication presents experimental studies of glued laminated timber beams reinforced with basalt-epoxy rods. GL24h wood (Table 1) and basalt epoxy BFRP bars (Table 2) were used to make the beams. The beams were subjected to a four-point bending test. The values of destructive forces are presented in Table 3.
1 Czestochowa University of Technology, Faculty of Civil Engineering, 3 Akademicka St., 42-218 Czestochowa, Poland,
Table 1
Characteristic values of strength and elasticity in N/mm2 and density in kg/m3 for homogeneous
glued laminated wood [7]
Properties Symbol Value
Bending strength fm,g,k 24 Tensile strength ft,0,g,k 19.2 ft,90,g,k 0.5 Compression strength fc,0,g,k 24 fc,90,g 2.5 Shear strength fv,g,k 3.5 Modulus of elasticity E0,g,mean 11 500 E0,g,05 9600 E90,g,mean 300 E90,g,05 250
Modulus of rigidity Gg,mean 650
Gg,05 540
Density ρg,k 405
ρg,mean 445
Table 2
Characteristic values of strength and elasticity for BFRP basalt-epoxy rods [8-10]
Properties Symbol Value [MPa]
Mean tensile strength for ϕ7 bars ffu 1184.97
Characteristic tensile strength for ϕ7 bars ffuk 1474.90
Mean tensile strength for ϕ9 bars ffu 817
Characteristic tensile strength for ϕ9 bars ffuk 1038
Modulus of elasticity ϕ7 for bars
Ef,śr
52800 Modulus of elasticity for ϕ9 bars 56300
Table 3
Comparison of the values of destructive forces obtained in analytical calculations with the val-ues obtained in experimental tests
Series Destructive force – analytical calculations
Destructive force –
experimental tests Difference Mean difference
(kN) (kN) (%) (%) A 53.32 55.25 –3.61 –17.06 53.32 56.26 –5.51 53.32 60.8 –14.02 B 54.10 67.92 –25.55 54.10 64.78 –19.75 54.10 58.3 –7.77 C 53.62 68.54 -27.83 53.62 65.42 –22.02 D 53.79 65.9 –22.51 53.79 64.25 –19.44 53.79 64.39 –19.70
2.2. Analytical calculations
In order to estimate the load
composites, a popular method was used in the calculations that is often presented in the liter ture [4, 5]. The assumptions and
structural elements.
The main assumptions of the adopted calculation model are shown in Figure 1. For the ca culations, the elastic and ideal elastic nature of the wood in compression was adopted the ideal elasticity in tension (Fig.
For BFRP basalt-epoxy rods, the elastic model was adopted for both tensile and compression (Fig. 2b).
Fig. 1. The adopted assumptions of the analytical model in cross section
a
Fig. 2. Material models used for analytical calculations:
Values of wood strength were adopted based on standard data [7], which are presented in Table 1. Due to the small dimensions of the samples tested experimentally, the values of bending and tensile strength were increased by 10% (
sions of Eurocode 5 [11]. In addition, based on the recommendations present increase in compressive strength (
In the calculations, an increasing coefficient value (α
[5], due to the beneficial effect of the reinforcement on the form of destruction.
bending strength of timber reinforced with BFRP bars was calculated according to formula 1. The longitudinal modulus of wood E
Analytical calculations
In order to estimate the load-bearing capacity of timber elements reinforced with fibrous composites, a popular method was used in the calculations that is often presented in the liter
5]. The assumptions and calculation procedures of the said method match the analyzed The main assumptions of the adopted calculation model are shown in Figure 1. For the ca culations, the elastic and ideal elastic nature of the wood in compression was adopted
the ideal elasticity in tension (Fig. 2a) was used, which is related to the wood characteristics. epoxy rods, the elastic model was adopted for both tensile and compression
The adopted assumptions of the analytical model in cross section
b
Material models used for analytical calculations: a) glulam, b) BFRP bars
Values of wood strength were adopted based on standard data [7], which are presented 1. Due to the small dimensions of the samples tested experimentally, the values of bending and tensile strength were increased by 10% (fm,g,ft,0,g), which is justified by the prov
sions of Eurocode 5 [11]. In addition, based on the recommendations presented in [5], a 10% increase in compressive strength (fc,0,g) was also assumed.
In the calculations, an increasing coefficient value (αm = 1.4) of bending strength was used
[5], due to the beneficial effect of the reinforcement on the form of destruction.
bending strength of timber reinforced with BFRP bars was calculated according to formula 1. The longitudinal modulus of wood E0,g,05 [7] was adopted, which allows the results closest to
bearing capacity of timber elements reinforced with fibrous composites, a popular method was used in the calculations that is often presented in the
litera-calculation procedures of the said method match the analyzed The main assumptions of the adopted calculation model are shown in Figure 1. For the cal-culations, the elastic and ideal elastic nature of the wood in compression was adopted, whereas
2a) was used, which is related to the wood characteristics. epoxy rods, the elastic model was adopted for both tensile and compression
Values of wood strength were adopted based on standard data [7], which are presented 1. Due to the small dimensions of the samples tested experimentally, the values of ), which is justified by the
provi-ed in [5], a 10% 1.4) of bending strength was used [5], due to the beneficial effect of the reinforcement on the form of destruction. Finally, the bending strength of timber reinforced with BFRP bars was calculated according to formula 1. [7] was adopted, which allows the results closest to
experimental research to be obtained. The data adopted for basalt-epoxy rods are presented in Table 2, and average values were used for the calculations.
,, , ,,, (1)
Due to the high strength of BFRP rods, two possible models of element destruction were assumed: by exceeding the limit of tensile strength of the wood fibres in the tension zone and by crushing timber fibres in the compression zone.
Load bearing capacity under tension
Based on the theoretical model (Fig. 1) and adopted material models (Fig. 2a, 2b) and the determination of the cross-sectional equilibrium (formula 2), it is possible to determine the position of the neutral axis (hc,t, hc,c). Calculation of the load capacity for both failure models
(Mt,f, Mc,f) is possible after determining the position of the neutral axis.
, , , , (2) , , , , , , (3) , , ,, ,, (4) , , ,, 2 ,, , 2 (5) , , , , , , (6) ,, 2 ,, 2 (7) (8) , (9) , , (10) , , (11)
After substituting formulas 3 - 11 for equation 2 and transforming relative to the variable hcf, the quadratic equation can be obtained.
After determining the position of the neutral axis, it is possible to: • determine the height of the plasticized zone,
• check the conditions for the deformation of reinforcing bars.
Knowing the position of the neutral axis and the height of the plasticized zone, it is possible to determine the cross-sectional force arm.
The tensile load failure model can be determined according to the formula:
/ , , , , , , , , , (12)
Load bearing capacity under compression
When compression failure is analyzed, it is assumed to exceed the limit value of plastic deformation for compression in timber. The value of plastic deformation has been assumed
equal to εc,u = 1.2% and εf,c
equation 2 is used and the quadratic equation obtained.
The load capacity due to compression can be determined on the basis of formula (12). The final value is the smaller of the two determined values for different destruction models:
3. Results
Based on the calculation procedures presented in the article, the values of destructive forces were determined for all series of reinforced beams. The comparison of the values of destructive forces determined theoretically and o
determination of the percentage differences in the results obtained is presented in Table 3. The correlation between the values from the experiment and the theoretical values is shown in Figure 3.
Fig. 3.
4. Discussion and conclusion
Based on the calculations carried out, it can be seen that: • The average difference between the values of destructiv
tests and theoretically determined values is with the values presented in other publications [4, 5].
• Based on theoretical calculations, the load capacity of the element is under
of cases, which is beneficial in engineering applications from the point of view of structural safety.
• Using the presented method to estimate the load capacity of beams has application possibil ties, but requires knowledge of the exact mat
• Assumptions were made in relation to the use of BFRP bars to strengthen the analyzed beams, for which there is no accurate material data. Therefore, the results obtained are not completely reliable.
Literature
[1] Jasieńko J., Połączenia klejowe w rehabilitacji i wzmacnianiu zginanych belek drewnianych, Oficyna Wydawn cza Politechniki Wrocławskiej, Wrocław 2002.
[2] Nowak T., Analiza pracy statycznej zginanych belek drewnianych wzmacnianych przy użyciu CFRP, doktorska, Wrocław 2007.
[3] Fossetti M., Minafò G., Papia M., Flexural behaviour of glulam timber beams reinforced with FRP cords, Construction and Building Materials 2015, 95, 54
f,c = 0 on the basis of [5]. As in the previous model, the
equation 2 is used and the quadratic equation obtained.
The load capacity due to compression can be determined on the basis of formula (12). The final value is the smaller of the two determined values for different destruction models:
Based on the calculation procedures presented in the article, the values of destructive forces were determined for all series of reinforced beams. The comparison of the values of destructive forces determined theoretically and on the basis of experimental tests, together with the determination of the percentage differences in the results obtained is presented in Table 3. The correlation between the values from the experiment and the theoretical values is shown
Fig. 3. Comparison of values of destructive forces obtained in analytical calculations and experimental tests
Discussion and conclusion
Based on the calculations carried out, it can be seen that:
The average difference between the values of destructive forces obtained in experimental tests and theoretically determined values is -17.06%. The obtained results are comparable with the values presented in other publications [4, 5].
Based on theoretical calculations, the load capacity of the element is underestimated in 94% of cases, which is beneficial in engineering applications from the point of view of structural Using the presented method to estimate the load capacity of beams has application possibil ties, but requires knowledge of the exact material characteristics of the designed elements. Assumptions were made in relation to the use of BFRP bars to strengthen the analyzed beams, for which there is no accurate material data. Therefore, the results obtained are not completely
Jasieńko J., Połączenia klejowe w rehabilitacji i wzmacnianiu zginanych belek drewnianych, Oficyna Wydawn cza Politechniki Wrocławskiej, Wrocław 2002.
Nowak T., Analiza pracy statycznej zginanych belek drewnianych wzmacnianych przy użyciu CFRP,
Fossetti M., Minafò G., Papia M., Flexural behaviour of glulam timber beams reinforced with FRP cords, Construction and Building Materials 2015, 95, 54-64.
0 on the basis of [5]. As in the previous model, the equilibrium The load capacity due to compression can be determined on the basis of formula (12). The final value is the smaller of the two determined values for different destruction models:
(13)
Based on the calculation procedures presented in the article, the values of destructive forces were determined for all series of reinforced beams. The comparison of the values of destructive n the basis of experimental tests, together with the determination of the percentage differences in the results obtained is presented in Table 3. The correlation between the values from the experiment and the theoretical values is shown
e forces obtained in experimental 17.06%. The obtained results are comparable estimated in 94% of cases, which is beneficial in engineering applications from the point of view of structural Using the presented method to estimate the load capacity of beams has application
possibili-erial characteristics of the designed elements. Assumptions were made in relation to the use of BFRP bars to strengthen the analyzed beams, for which there is no accurate material data. Therefore, the results obtained are not completely
Jasieńko J., Połączenia klejowe w rehabilitacji i wzmacnianiu zginanych belek drewnianych, Oficyna
Wydawni-Nowak T., Analiza pracy statycznej zginanych belek drewnianych wzmacnianych przy użyciu CFRP, Rozprawa
[4] Borri A., Corradi M., Grazini A., A method for flexural reinforcement of old wood beams with CFRP materials, Composites: Part B 2005, 36, 143-153.
[5] Yang H., Liu W., Lu W., Zhu S., Geng Q., Flexural behavior of FRP and steel reinforced glulam beams: Experi-mental and theoretical evaluation, Construction and Building Materials 2016, 106, 550-563.
[6] Rajczyk M., Jończyk D., Badania belek z drewna klejonego warstwowo wzmocnionych prętami bazaltowo– epoksydowymi, Zeszyty Naukowe Politechniki Częstochowskiej. Seria Budownictwo 2018, 24, 298+304. [7] PN–EN 14080:2013 Konstrukcje drewniane –– Drewno klejone warstwowo i drewno lite klejone warstwowo
– Wymagania.
[8] Szymczak P., Olbryk P., Chołostiakow S., Kamińska M., Badanie betonowych belek zbrojonych prętami kompo-zytowymi, Wyniki badania belek zbrojonych prętami GFRP i BFRP. Sprawozdanie z badań.
[9] Szymczak P., Olbryk P., Chołostiakow S., Kamińska M., Badanie przyczepności prętów kompozytowych GFRP i BFRP do betonu, Wyniki badania próbek zbrojonych prętami GFRP i BFRP. Sprawozdanie z badań.
[10] Szymczak P., Olbryk P., Chołostiakow S., Kamińska M., Badanie prętów kompozytowych, Wyniki badania prętów kompozytowych GFRP i BFRP. Sprawozdanie z badań.
[11] PN-EN 1995-1-1:2010 Eurokod 5: Projektowanie konstrukcji drewnianych – Część 1-1: Postanowienia ogólne i reguły dotyczące budynków.
Obliczanie nośności belek z drewna klejonego warstwowo
zbrojonych BFRP
STRESZCZENIE:
Wzmacnianie elementów drewnianych z wykorzystaniem kompozytów włóknistych jest coraz szerzej stosowanym rozwiązaniem w budownictwie. Pomimo zwiększającej się popularności rozwiązania nadal brakuje przepisów normatywnych. W artykule oszacowano przydatność powszechnie znanej metody okreś- lania nośności wzmacnianych elementów drewnianych do obliczania belek z drewna klejonego warstwowo wzmacnianych materiałami BFRP. Porównano wartości nośności obliczone analitycznie z wartościami wyznaczonymi w badaniach eksperymentalnych. Metoda przedstawiona w artykule może być pomocna z inżynierskiego punktu widzenia.
SŁOWA KLUCZOWE:
